An irritated Mayor Giuliani branded the Port Authority as inept in dealing with the storm yesterday that shut all three major airports – and he slammed the agency for not cooperating with city officials.

“It seems to me they are not doing a good job of coordinating,” Giuliani said from the city’s command center at the Office of Emergency Management.

“People are stranded at the airport. You have some airplanes that have been sitting on the runway for two, 2½ hours . . . and the people sitting on them are quite frustrated,” he said.

“We know of one case because it’s the mother-in-law of a high-ranking police official who has called several times on her cell phone to say – and I’m not sure I can express it the right way – that she’s quite angry,” Giuliani said.

That high-ranking cop is First Deputy Commissioner Joseph Dunne, sources told The Post.

The Port Authority is operated by both the states of New York and New Jersey and operates the three major area airports, and bridges and tunnels that cross the Hudson River.

The mayor was also peeved the agency did not send its representatives to the ultra-modern command center in the World Trade Center – where the PA is headquartered – until about six hours after the storm began.

“The Port Authority does not coordinate with other people. We have every city agency here, state agencies and even federal representation. The Port Authority showed up about 15 minutes ago,” fumed Giuliani, who has often accused the PA of making more money from New York’s airports than it puts back in.

“If the PA were more cooperative, you could help with things like transportation to and from the airport. We have the ability to assist with that. If they were here throughout the night, then there’s an awful lot of help that we can offer them.”

Giuliani’s tirade came moments after his press briefing, when he returned to the podium to give out a phone number for stranded airline passengers looking for hotel rooms.

A PA spokesman, Steven Coleman, contended that agency representatives do not need to be physically at the center to be cooperative.

“We have been in constant telephone contact with OEM and they have been kept abreast of our efforts,” Coleman said. “We’ve had someone in his bunker since about 10 a.m.”

La Guardia general manager Warren Kroeppel also said airport officials have been in constant contact with the city.

The mayor told reporters the PA sergeant and lieutenant who showed up came only after some arm-twisting – in the form of calling the governor’s office.

“Cooperation does not alleviate all the problems of an emergency, but it alleviates some of it. People go kind of crazy when they sit on a runway for 2½ hours in good weather or bad weather,” Giuliani said.